# How we can prove boltzman constant?

1. Jun 12, 2010

### phys111

hello all

if some one here can help me to prove boltzman costant

from SI unit to reach that k= 1.0356 x 10-22 Torr-liter/K ?

2. Jun 12, 2010

### alxm

I don't know how you can 'prove' an experimental value. But I can tell you how to measure it.

Simplest way would just be to measure the Ideal Gas Constant, since that's just Boltzmann's constant in disguise ($$R = N_Ak_B$$). Take a fixed amount of a relatively ideal gas (e.g. helium) at a fixed volume. Vary the temperature and measure the pressure. Plot p against T and the slope is N*kB.

3. Jun 12, 2010

### phys111

thanks

but i need just to calculate it ?

4. Jun 12, 2010

### alxm

I don't know what you expect to calculate it from? It's a physical constant, not a mathematical one. It's the fundamental relationship between energy and temperature. For different units of either, it wouldn't be needed at all.

The Kelvin scale of temperature is defined by the triple point of water, and so the Boltzmann constant in SI units is determined by that as well.

5. Jun 12, 2010

### phys111

we can start from this relation

PV=N KT

& use convert from SI unit to This unit but i dont reach for the same result

6. Jun 12, 2010

### alxm

Oh sorry, I thought you meant to somehow calculate it. You're saying you want to convert units.

Well if your pressure and volume is in SI units, pV = Pa*m3, so if you want it in Torr-liters you want to multiply by Pascal/Torr and liters/m3.
So (1/133.322368)*1000.

So 1.3806504E-23 (Pa*m3) =1.380 6504E-23*(1000/133.322368) (Torr*Liters) = 1.03513E-22 (Torr*Liters)

7. Jun 13, 2010

### phys111

yes , right

but i dont understand
1.3806504E-23 (Pa*m3)
how you found it
if u can explane to me more

8. Jun 13, 2010

### Redbelly98

Staff Emeritus
That is the accepted value in SI units, which anybody can find using Google. The value is given by many sources:
It is not clear what the source of your confusion is. Do you want to know:
• How is k determined experimentally?
• Where can you look up the value of k?
• Why are the units Pa*m3/K ?
• Other?

9. Jun 15, 2010

### phys111

thanks

we can find that from Boyle's Law

right